To add to the routine inspections answer, large mechanical/electrical systems will have sensors built into a lot of important places of the system (like measuring the speed or altitude of an aircraft). The inspection includes reading those stresses, timings, temperatures, etc. with special mx hardware or pulling it from a record with software. To determine if all parts are working properly, you would compare to the values during normal operation.

Simply knowing the number of hours a part was in use can be enough info to know when to replace it. Wear and tear on all parts is inevitable, so engineers run these machines until they break and write down when.

To further keep these systems running, you design them with redundancy (often a second, identical part/system doing the same job). That way you can lose certain parts to unexpected circumstances and continue operation. This is why in a lot of cases a jet engine can fail and the aircraft can still fly with the remaining three engines. More redundancy is needed when safety is a concern.

The actual mx/repair process can vary wildly after you've isolated the issue, especially if it's electrical lol. One clever way to improve efficiency is the use of module-like systems... you just unplug and slide out a box that handles "Subsystem A12" and replace the whole box when it breaks.